Acceleration of a brick, involving integrals

1. The problem statement, all variables and given/known data
A 15 kg brick moves along an x axis. Its acceleration as a function of its position is shown in Fig. 7-32. What is the net work performed on the brick by the force causing the acceleration as the brick moves from x = 0 to x = 8.0 m?

2. Relevant equations
W = FΔx = max

3. The attempt at a solution
I haven't taken calculus prior to the class(am taking it now), and I was just introduced to integrals today by a friend. He showed me how to integrate another Work problem, where F = -6x. I understood that it would integrate into -3x2 + C, and I found C. My question is how would I go about this one?

You don't need to know integration techniques. It is enough to understand that the value of the (definite) integral of a function represents the area under the graph of the function.
Here is a lot more straightforward to calculate the area (as all the segments are straight lines).

I mean, it seems rudimentary that the net work is the area under the curve times mass, since
the area under the curve is aΔx, and multiplying by m gives you maΔx, which equals work.
And yet, that was wrong.